NCERT Class XI Mathematics - Relations and Functions - Solutions
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Question : 33
Total: 36
Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b 2
Are the following true?
(i) (a, a) ∈ R, for all a ∈ N
(ii) (a, b) ∈ R, implies (b, a) ∈ R
(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.
Are the following true?
(i) (a, a) ∈ R, for all a ∈ N
(ii) (a, b) ∈ R, implies (b, a) ∈ R
(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.
Solution:
We have, R = {(a, b) : a, b ∈ N and a = b2} = {(b2, b) : b ∈ N}
(i) False
Only when a = 1, (a, a) = (1, 1) = (12, 1) ∈ R.
(ii) False
If (a, b) ∈ R ⇒ a =b 2 a 2
∴ (a, b) ∈ R ⇒ (b, a) ∉ R.
(iii) False
If (a, b) ∈ R ⇒ a =b 2
and (b, c) ∈ R ⇒ b =c 2
From (i) and (ii), a =( c 2 ) 2 c 4 c 2
⇒ (a, b) ∈ R and (b, c) ∈ R but (a, c) ∉ R.
(i) False
Only when a = 1, (a, a) = (1, 1) = (12, 1) ∈ R.
(ii) False
If (a, b) ∈ R ⇒ a =
∴ (a, b) ∈ R ⇒ (b, a) ∉ R.
(iii) False
If (a, b) ∈ R ⇒ a =
and (b, c) ∈ R ⇒ b =
From (i) and (ii), a =
⇒ (a, b) ∈ R and (b, c) ∈ R but (a, c) ∉ R.
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